by Trump
Roll Through the Ages really isn't anything like the rest of the games you've listed. It follows the traditional dice game mold of getting a few re-rolls and then scoring what you end up with.Kingsburg gives you some flexibility with what you get for your die rolls, but the game is going to favor someone who rolls higher a lot more than the other players. You can't really plan in the game. If you want some gold next turn, you just hope to roll something that will get you on to a gold space.
Alien Frontiers cares less about how high you roll and more about the pattern you roll. Sure, there are still spots where bigger is better, but you're rewarded for rolling sets as well. If you like, you can pick up artifacts during the game that will let you manipulate your die rolls to create those patterns. And the scoring is based more on are majorities on the board than it is rolling some great combo.
Castles of Burgundy isn't like any of these. You have a number of options for how you use the dice you roll. The size of the number doesn't matter at all. The dice act more like... keys. For example, maybe you roll a 2 and a 4. So you can pick up a piece only from those bins, you can place to your board only on those numbers, and you can sell only that type of good. You use worker chips to +/-1 on your die roll. Collect a few of those workers and then when you really WANT to hit a certain number then you can be sure to do so. Good players try to set themselves up for ANY die rolls.
Burgundy is the least luck-based of all of these games. Each turn is more akin to solving a puzzle than anything else.